Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2

Average Error: 0.1 → 0.1

Time: 42.8s

Precision: binary64

Cost: 6848

Math

\[\left(x \cdot \log y - z\right) - y \]

↓

\[\left(x \cdot \log y - z\right) - y \]

FPCore

(FPCore (x y z) :precision binary64 (- (- (* x (log y)) z) y))

↓

(FPCore (x y z) :precision binary64 (- (- (* x (log y)) z) y))

C

double code(double x, double y, double z) {
	return ((x * log(y)) - z) - y;
}

↓

double code(double x, double y, double z) {
	return ((x * log(y)) - z) - y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * log(y)) - z) - y
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * log(y)) - z) - y
end function

Java

public static double code(double x, double y, double z) {
	return ((x * Math.log(y)) - z) - y;
}

↓

public static double code(double x, double y, double z) {
	return ((x * Math.log(y)) - z) - y;
}

Python

def code(x, y, z):
	return ((x * math.log(y)) - z) - y

↓

def code(x, y, z):
	return ((x * math.log(y)) - z) - y

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * log(y)) - z) - y)
end

↓

function code(x, y, z)
	return Float64(Float64(Float64(x * log(y)) - z) - y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * log(y)) - z) - y;
end

↓

function tmp = code(x, y, z)
	tmp = ((x * log(y)) - z) - y;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]

Derivation

1. Initial program 0.1

   \[\left(x \cdot \log y - z\right) - y \]

2. Final simplification 0.1

   \[\leadsto \left(x \cdot \log y - z\right) - y \]

Alternatives

Alternative 1
Error	9.9
Cost	7380

\[\begin{array}{l} t_0 := \log y \cdot x\\ t_1 := t_0 - z\\ t_2 := t_0 - y\\ \mathbf{if}\;z \leq -6.1 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+99}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	9.7
Cost	7248

\[\begin{array}{l} t_0 := \left(-z\right) - y\\ t_1 := \log y \cdot x\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+142}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+49}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+66}:\\ \;\;\;\;t_1 - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	13.5
Cost	6856

\[\begin{array}{l} t_0 := \log y \cdot x\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+84}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+128}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	31.6
Cost	392

\[\begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+80}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-30}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 5
Error	22.0
Cost	256

\[\left(-z\right) - y \]

Alternative 6
Error	42.0
Cost	128

\[-y \]

Reproduce

herbie shell --seed 2023099 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))